Certainly the 7mm-08 can take all the game just as well as the 7x57 Mauser has done for over 100 years, but out in the open, I would use a 7x64 or .280 Rem - something in the .30-06 class. It is really a matter of range; the 7x64 delivers energy like being 100 yards closer than a 7mm-08, and only the more rounded flat-base 160-grs seat to the bottom of the neck and permit more powder in the 7mm-08. It is 160 and 175-gr 7mm bullets I would want to use on larger animals, like elk here in the USA.
So I would talk to the outfitter and PH about the terrain, expectations of types of shots and distance, and what they think of the 7mm-08 and 7x57 for the larger plains game. And your friend is surely taking a larger rifle to Africa, as well, like a .375 H&H and maybe something in between it and the 7mm-08.
----- historical PS:
James Corbett used a 7x57 to kill several man-eating tigers, and a leopard at close range... not his first choice, however.
Eleanor O'Connor took all kinds of African game, elk and sheep with her 7x57. She also used her "big gun", a .30-06, on larger antelope. Jack loaded a 165-gr Hornady ( discontinued ) at 2,650 fps, and 160-gr Sierra and Speer ( Speer was a neighbor and friend of the O'Connors) at 2,660 fps, using surplus 4831 powder. It was a Mauser with a 22-inch barrel, described by O'Connor in his book on big game rifles, under a photo caption:
"Bradford O'Connor shooting a fine, lightweight mountain rifle owned by the author. It is a 7x57 built on a Czech VZ-24 action. Floor plate has been hinged with release button in the trigger guard, bolt handle altered, Sukalle safety installed. Scope is Weaver K-4 [later replaced by a
Leupold 3x] on Buehler mount. Barrel and metal work was done by Tom Burgess, Spokane, Russ Leonard of Spokane built the light, handsome stock. Complete rifle weighs 8 lbs on the nose and is a joy to carry and to shoot."